Because we borrow much of our theoretical framework from [1]}, we also leverage their simulation framework as a useful point of comparison.
We draw independent samples \(X \sim \mathcal {N}(0,I_{4 \times 4})\)  and generate a binary outcome \(Y \sim \text{Bernoulli}(\Phi (X\beta ))\)  where \(\beta = (2.5, 3.5, 0, 0)\) . Because the outcome is binary, we use accuracy as our predictive skill measure, and the true VI values are given by (0.136, 0.236, 0, 0), respectively.
We first directly compare the LazyVI and retrain estimators by estimating \(\text{\sc vi}\)  across 100 simulated datasets of sample size \(n=1000\)  and computing the empirical 95% confidence intervals. In Figure REF , we see that the LazyVI and retrain estimates both achieve the desired level of coverage with low bias.
In this simulation, LazyVI took on average 0.6 seconds (including cross-validating to find the optimal ridge parameter), while retraining took \(7.5\)  seconds. In this setting, LazyVI is just as accurate as retraining with a more than 10x speed-up.
<FIGURE>